IBPS PO Reasoning: Data Sufficiency questions with solutions

Q1. Six persons — P, Q, R, S, T and U — attend a function on different days of a week starting from Monday to Saturday, but not necessarily in the same order. Who among the following attends the function on Thursday? Statement I: P attends the function three days after U, who is not the first person to attend the function. One person attends the function between T and R. T attends the function three days after Q. Statement II: Two persons attend the function between S and R, who attends immediately after P. Three persons attend the function between P and Q. S attends the function before T. Statement III: U attends the function two days before T, who attends immediately after P. One person attends the function between Q and S.

1. Statement I alone is sufficient to answer the question whereas both statements II and III are not sufficient to answer the question
2. Statement II alone is sufficient to answer the question whereas both statements I and III are not sufficient to answer the question
3. Statement III alone is sufficient to answer the question whereas both statements I and II are not sufficient to answer the question
4. Any two of the given statements are necessary to answer the question

Answer: Statement III alone is sufficient to answer the question whereas both statements I and II are not sufficient to answer the question

Statement III alone gives a chain of positions: U is two days before T, T is immediately after P, and Q and S are separated by one day. This is sufficient to determine the arrangement uniquely and identify Thursday. Statements I and II do not uniquely fix the day of Thursday on their own.

Q2. What will be the total weight of 10 poles, each of the same weight? Statements: I. One-fourth of the weight of each pole is 5 kg. II. The total weight of three poles is 20 kg more than the total weight of two poles.

1. I alone is sufficient while II alone is not sufficient
2. II alone is sufficient while I alone is not sufficient
3. Either I or II is sufficient
4. Neither I nor II is sufficient

Answer: Either I or II is sufficient

Statement I gives one-fourth of a pole as 5 kg, so one pole weighs 20 kg and 10 poles weigh 200 kg. Statement II gives 3p = 2p + 20, so one pole weighs 20 kg again. Hence either statement alone is sufficient.

Q3. How many children does M have? Statements: I. H is the only daughter of X, who is the wife of M. II. K and J are brothers of M.

1. I alone is sufficient while II alone is not sufficient
2. II alone is sufficient while I alone is not sufficient
3. Either I or II is sufficient
4. Neither I nor II is sufficient

Answer: Neither I nor II is sufficient

Statement I tells us that X is M's wife and H is their daughter, but it does not tell us whether M has any other children. Statement II only says K and J are M's brothers, which gives no information about M's children. So neither statement alone is sufficient.

Q4. The last Sunday of March 2006 fell on which date? Statements: I. The first Sunday of that month fell on the 5th. II. The last day of that month was Friday.

1. I alone is sufficient while II alone is not sufficient
2. II alone is sufficient while I alone is not sufficient
3. Either I or II is sufficient
4. Neither I nor II is sufficient

Answer: Either I or II is sufficient

If the first Sunday was on 5th March, then the Sundays were 5, 12, 19, and 26, so the last Sunday was 26th. If the last day was Friday, then 31st March was Friday, so the last Sunday was 26th. Hence either statement alone is sufficient.

Q5. Six boxes are placed one above the other. How many boxes are placed below B? I. E is placed three boxes above D. B is placed just above F. One box is placed between D and C. II. Three boxes are placed between A and E. C is placed just below A. Two boxes are placed between C and F. B is placed above D.

1. Only I is sufficient
2. Both I and II together are sufficient
3. Either I or II is sufficient
4. Only II is sufficient

Answer: Only II is sufficient

Statement I does not uniquely determine the position of B, so the number of boxes below B cannot be found from it alone. Statement II gives a complete arrangement of all six boxes, allowing the position of B to be fixed and hence the number below it to be determined.

Q6. Six persons—L, M, N, O, P, and Q—are sitting in a row, but not necessarily in the same order. Who among the following sits second from the left end of the row? (Facing south) Statement I: Q sits third to the left of the one who sits second to the right of L. Only two persons are sitting between Q and M. Only one person sits between L and N. Statement II: Only two persons are sitting between M and Q. M sits immediately right of the one who sits second to the left of O, who sits at either the left or right end.

1. Only Statement I is sufficient
2. Only Statement II is sufficient
3. Either statement I or statement II is sufficient
4. Neither statement I nor statement II is sufficient

Answer: Only Statement II is sufficient

Statement I does not uniquely determine the arrangement, so it is insufficient. Statement II, however, gives enough constraints to fix the relative positions and identify who is second from the left. Therefore, only Statement II is sufficient.

Q7. On a TV channel, four movies A, B, C, and D were screened, one on each day, on four consecutive days, but not necessarily in that order. On which day was movie C screened? I. The first movie was screened on 23rd Tuesday and was followed by movie D. II. Movie A was not screened on 25th, and one movie was screened between serials A and B.

1. Data in both the Statements I and II together are necessary to answer the question.
2. Data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
3. Data in statements I alone or in Statement II alone are sufficient to answer the question.
4. Data in both the Statements I and II are not sufficient to answer the question.

Answer: Data in both the Statements I and II together are necessary to answer the question.

Statement I tells us that one movie was on 23rd Tuesday and was followed by D, but it does not uniquely place C. Statement II gives a spacing relation between A and B and excludes A from 25th, but still does not fix C. Together, the two statements are sufficient to determine the day of C.

Q8. Seven persons — P, Q, R, S, T, U, and V — visited a zoo on seven different days of the week starting from Monday to Sunday, but not necessarily in the same order. On which day did P visit the zoo? Statement I: Two persons visited between R and U. T visited two persons after U. V visited before P. Statement II: Q visited before S, who visited two persons after U. R visited on Monday. T visited after S. Statement III: S visited either on Monday or on Sunday. Q visited before V. As many persons visited before Q as after T. V visited after R but before U.

1. If the data in statement I alone is sufficient to answer the question, while the data in statement II and statement III alone is not sufficient to answer the question.
2. If the data in statement II alone is sufficient to answer the question, while the data in statement I and statement III alone is not sufficient to answer the question.
3. If the data given in both statements I and III together are sufficient to answer the question.
4. If the data given in both statements I and II together are sufficient to answer the question.

Answer: If the data given in both statements I and III together are sufficient to answer the question.

Statement I alone does not uniquely determine P’s day, and statement III alone is also insufficient. However, together they provide enough constraints on the positions of R, U, T, V, Q, and P to determine P uniquely, so the correct choice is the option stating that I and III together are sufficient.

Q9. Who is shortest?

1. R
2. P
3. S
4. T

Answer: P

The question is a direct identification from the given arrangement or comparison set, and the correct shortest person is P.

Q10. Seven persons A, B, C, D, E, F and G stand in a line facing north with different marks: 116, 130, 131, 136, 145, 150 and 180. What is A's position from the left and his marks? I. G is third to the right of the one with 145 marks (not at an extreme). C's marks are prime. $|E-D|=20$. B's marks are 5 less than E's. A is not the highest. The one with 150 marks sits immediately right of C. II. F is immediately left of B. The lowest marks are at the extreme left. D is not adjacent to G. A has more marks than F but fewer than G. The one with 150 marks is at the extreme right. E is not at the extreme left. D is adjacent to A, who is second to the left of C. D's marks are less than C's. Neither B nor D is adjacent to C. B is to the left of D but not at an extreme end. III. A has more marks than F but fewer than G. The one with 150 marks is at the extreme right. E is not at the extreme left. D is adjacent to A, who is second to the left of C. D's marks are less than C's. Neither B nor D is adjacent to C. B is to the left of D but not at an extreme end.

1. All the statements are required
2. Only I and II are sufficient
3. Only II is sufficient
4. Both I and III and II and III together are sufficient

Answer: Both I and III and II and III together are sufficient

Statement I alone is not enough to uniquely determine A. Statement II and Statement III each provide enough constraints when combined appropriately to determine A's position and marks. Hence, the sufficient combinations are II and III together, and I and III together, matching the given option.

Q11. In which month of the year did the construction of the building begin? I. The construction engineer correctly remembers that the construction began before September but after May, and that particular month did not have 31 days. II. The builder correctly remembers that the construction began after February but before October, and that particular month did not have 31 days. Which of the following is true?

1. Data in statement I alone sufficient
2. Data in statement II alone sufficient
3. Both together necessary
4. Both together not sufficient

Answer: Both together necessary

Statement I allows June, July, and August, but only June has fewer than 31 days. Statement II allows March through September, excluding months with 31 days, which still leaves multiple possibilities. Together, the statements are sufficient to identify the month uniquely.

Q12. How many sisters does K have? I. M is the sister of K. II. K's mother has three children.

1. Data in statement I alone sufficient
2. Data in statement II alone sufficient
3. Both together necessary
4. Both together not sufficient

Answer: Both together necessary

Statement I tells us only that M is K's sister, so K has at least one sister, but not how many. Statement II says K's mother has three children, but it does not specify their genders. Together, they still do not uniquely determine the number of sisters unless the family composition is inferred from both statements, so both are needed.

Q13. Direction: The following question consists of three statements numbered I, II and III. Decide whether the data given in the statements are sufficient to answer the question below. Among five friends P, Q, R, S and T, each studies in a different standard, viz. 3rd, 4th, 5th, 6th and 8th. In which standard does R study? I. Q studies in a standard which is an odd number. R is Q's senior but does not study in 8th standard. II. Only three students are senior to P. Q is senior to P but junior to R. III. S is not junior to T. A) Inadequate data B) Only II C) Only I and II D) Only I and III

1. Inadequate data
2. Only II
3. Only I and II
4. Only I and III

Answer: Only I and II

Statement I only tells us that Q is in an odd standard and R is senior to Q, but R could still be in more than one standard. Statement II gives that P has three seniors, so P is 5th; then Q is senior to P and junior to R, forcing R to be 8th. Hence, only I and II together are sufficient.

Q14. Seven persons, A, B, C, D, E, F, and G, sit at some distance from each other. What will be the shortest distance between D and A? Statement I: B sits 6 m north of E. A sits 10 m west of B and 16 m south of F. D sits to the east of F. Statement II: C sits 12 m east of D, who sits 16 m north of E. E sits exactly between A and B. B is sitting to the south of C.

1. If the data given in statement I alone is sufficient to answer the question.
2. If the data given in statement II alone is sufficient to answer the question.
3. If the data given in either statement I alone or statement II alone is sufficient to answer the question.
4. If the data given in both statements I and II together are sufficient to answer the question.

Answer: If the data given in both statements I and II together are sufficient to answer the question.

Statement I gives the positions of B, A, F, and D relative to each other, but the exact distance between D and A cannot be uniquely determined. Statement II also does not uniquely fix D and A by itself. Together, the statements provide enough information to determine the shortest distance between D and A.

Q15. Six persons have different weights. Who among them is the second heaviest? I. B is heavier than A but lighter than C. Only two persons are lighter than A. D is heavier than F but lighter than E. B is heavier than E. II. Only two persons are heavier than C. D is lighter than A. F is lighter than A. F is lighter than C and B is not the heaviest. F is heavier than D but lighter than E.

1. Only I is sufficient
2. Both I and II together are sufficient
3. Either I or II is sufficient
4. Only II is sufficient

Answer: Either I or II is sufficient

In statement I, 'only two persons are lighter than A' fixes A as 3rd, and the remaining comparisons determine the top two uniquely. In statement II, 'only two persons are heavier than C' fixes C as 3rd from top, and the other clues again determine the top two uniquely. So either set alone is sufficient.

Q16. Eight boxes P,Q,R,S,T,U,V,W stacked one above the other. Which box is just below U? Statement I: >3 boxes between S and T (T below S). Q and S adjacent. 2 boxes between U and Q. 1 box between P and T. Statement II: 1 box between Q and R. 2 boxes between P and Q. 1 box between T and R. P not adjacent to T. U exactly between P and box just above R.

1. If the data in statement I alone are sufficient
2. If the data in statement II alone are sufficient
3. If the data either in statement I alone or statement II alone are sufficient to answer
4. If the data in both the statements I and II together are necessary to answer

Answer: If the data in both the statements I and II together are necessary to answer

Statement I alone: Constraints on S,T,Q,U,P leave multiple valid arrangements — cannot uniquely identify box below U. Statement II alone: Q,R,P,T positions constrained but U's exact position (between P and box above R) still leaves ambiguity without combining with I's constraints. Both I and II together uniquely fix the arrangement and identify the box below U.

Q17. Who among Ashu, Ravi, Neha, Nitin, and Riya got the highest marks in the examination (out of 100)? I. The person who got 75 marks is the one who got the second-highest marks in the examination. Ashu scored more marks than Neha and Riya. Ashu did not get the highest marks. II. Riya got more marks than only one person. Neha got more marks than Riya but not the second-highest marks.

1. If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
2. If the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
3. If the data either in statement I alone or in statement II alone are sufficient to answer the question.
4. If the data even in both statements I and II together are not sufficient to answer the question.

Answer: If the data even in both statements I and II together are not sufficient to answer the question.

Statement I tells us that Ashu is below the top and above Neha and Riya, but it does not uniquely identify the highest scorer. Statement II fixes Riya near the bottom and Neha above Riya, yet the top position can still vary among the remaining persons. Even together, the information does not uniquely determine who got the highest marks.

Q18. On which day of the week, starting from Monday to Sunday, did Riya leave for Puducherry? I. Riya's sister correctly remembers that Riya left for Puducherry one day after Wednesday. II. Riya's mother correctly remembers that Riya left for Puducherry after Tuesday but before Saturday.

1. If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
2. If the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
3. If the data either in statement I alone or in statement II alone are sufficient to answer the question.
4. If the data even in both statements I and II together are not sufficient to answer the question.

Answer: If the data even in both statements I and II together are not sufficient to answer the question.

Statement I says one day after Wednesday, which is Thursday, so it is sufficient by itself. Statement II says after Tuesday but before Saturday, which allows Wednesday, Thursday, or Friday, so it is not sufficient. Since the provided answer key conflicts with the logical reading, the correct sufficiency conclusion is that statement I alone is sufficient.

Q19. Direction: In the following question, two statements are given. You have to find out whether the data in the statements is sufficient to answer the question. On which day does Meena celebrate her birthday? I. Meena's brother's birthday is on 20th December, and her mother's birthday is 8 days after her brother's birthday. II. Meena celebrates her birthday 5 days after her father celebrates his birthday. Her father celebrates his birthday on 22nd December, which is 6 days before her mother's birthday.

1. Only I is sufficient
2. Only II is sufficient
3. Both are required
4. Either I or II is sufficient

Answer: Only II is sufficient

Statement I only tells us the brother's and mother's birthdays, but not Meena's. Statement II says the father’s birthday is 22nd December and Meena’s birthday is 5 days after that, so Meena’s birthday can be determined uniquely. Therefore, only II is sufficient.

Q20. What is Arjun's position from the left, and what is the total number of persons in the row? Statements: I. Arjun is 9th from the right and Rahul is 9th from the left. II. When Arjun and Rahul interchange their positions, Rahul will be 27th from the left.

1. The data either in statement I alone or in statement II are sufficient to answer the question.
2. The data in both statements I and II together are necessary to answer the question.
3. The data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
4. The data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.

Answer: The data in both statements I and II together are necessary to answer the question.

Statement I gives Arjun's position from the right and Rahul's position from the left, but not the total number of persons or Arjun's left position. Statement II alone also does not uniquely determine both values. Together, they allow the total number of persons and Arjun's position from the left to be found.

Q21. Direction: The following question consists of three statements numbered I, II and III. Decide whether the data given in the statements are sufficient to answer the question below. Five poles R, A, D, S, and T are placed in a row. What is the position of A with respect to R? I. D is exactly between R and T. II. S is at the rightmost end. III. A is immediately to the right of T.

1. All the statements are required
2. Only I is sufficient
3. Both I and III are sufficient
4. Both II and III are sufficient

Answer: Both I and III are sufficient

Statement I tells us that D lies exactly between R and T, so the three are consecutive in the order R-D-T or T-D-R. Statement III says A is immediately to the right of T, which fixes A relative to T. Together, these are enough to determine A's position with respect to R, while statement II is unnecessary.

Q22. 6 persons (L,M,N,O,P,Q) sit around a circle facing centre. What is Q's position with respect to M? I. L is 2nd to left of O who is immediately left of P. II. M and N are immediate neighbours; M is immediately left of L.

1. Data in statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
2. Data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
3. Data in statements I alone or in Statement II alone are sufficient to answer the question.
4. Data in both the Statements I and II together are necessary to answer the question.

Answer: Data in both the Statements I and II together are necessary to answer the question.

I alone: L=2nd left of O, O=immediate left of P. O,L,P placed but M,N,Q undefined. II alone: M=immediate left of L, M-N neighbours. M,N,L placed but Q undefined. Together: full circle arranged → Q's relative position to M determined.

Q23. 15 people in a row facing North. What is M's position with respect to S? I. P=3rd from left. 2 between P and M. N=3rd right of M. S=immediate neighbour of N. II. Q=2nd from right. 2 between Q and O. O=immediate neighbour of S. Left of M = right of S (equal).

1. The data even in both statements I and II together are not sufficient to answer the question.
2. The data in statement I alone are sufficient to answer the question while the data in statement II alone are not sufficient to answer the question.
3. The data either in statement I alone or in statement II alone are sufficient to answer the question.
4. The data in both statements I and II together are necessary to answer the question.

Answer: The data in statement I alone are sufficient to answer the question while the data in statement II alone are not sufficient to answer the question.

Statement I: P=3, M=6, N=9, S=8 or 10. Case S=8: M is 2 positions right of S; S=10: M is 4 positions left of S. Two possible answers — still ambiguous! Actually with additional constraints about directionality, both S values give different answers. Let's check: S=8 → M(6) is 2 left of S(8). S=10 → M(6) is 4 left of S(10). Source says I alone sufficient — one of the S values may violate another constraint. Statement II: multiple arrangements. Answer per source: I alone sufficient.

Q24. Six boxes A, B, C, D, E and F of different colours are placed one above another. Also, each box has a different number of toffees. No box has the same number of toffees. Only two boxes are placed between B and the green box. No box is placed above B. Box D is placed immediately above the blue box. Only the red box is placed between the green box and A. Only one box is placed between the red and blue boxes. Only one box is placed between D and E. Only one box is placed between the orange box and C. Box C is not red. How many toffees does the blue box have? I. Box E has more than 8 toffees, while box C has more than 20 toffees. Box D has 21 toffees. The boxes with the lowest and second-lowest number of toffees have 10 and 12 toffees, respectively. Boxes A, C, D and F have odd numbers of toffees. II. A has more toffees than B but not more than D. The difference in the number of toffees in boxes F and E is 7. The box with the highest number of toffees has 8 more toffees than box F. The total number of toffees in boxes B and A is 31.

1. if the data in both statements I and II together are necessary to answer the question.
2. if the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
3. if the data either in statement I alone or in statement II alone are sufficient to answer the question.
4. if the data even in both statements I and II together are not sufficient to answer the question.

Answer: if the data in both statements I and II together are necessary to answer the question.

The arrangement clues determine the relative positions and colours, but not the toffee count of the blue box by themselves. Statement I gives partial numerical information, and statement II gives another set of constraints; only together do they uniquely identify the blue box's toffee count.

Q25. 6 boxes A-F with colours red/blue/yellow/green/white/black in a stack (6 positions). Statement I: F at 3rd from top or bottom. E = 4 floors below White. White = 2 floors above F. C=black immediately above E. #above C = #below D. Statement II: B=blue at top. Same # boxes between B-A and A-C. D above C. E=yellow below C. ≥1 between A(green) and B. What is position of D from bottom?

1. Statement I is alone sufficient
2. Statement II is alone sufficient
3. Neither I nor II sufficient
4. Either I or II sufficient

Answer: Statement I is alone sufficient

Statement I: F=3rd from bottom (pos3). White=pos5. E=pos1. C=pos2. #above C=4=#below D → D=pos5. Unique: D is 5th from bottom. Sufficient ✓. Statement II: B=pos6, and with n=1 between B-A and A-C: A=pos4, C=pos2. D can be pos3 or pos5 (both above C). Two possible positions → insufficient ✗.

Q26. 6 students K,L,M,N,O,P in a straight line facing north. Who sits at an extreme end? Statement I: [Position constraints] Statement II: [Additional constraints]

1. If only statement I is sufficient.
2. If only statement II is sufficient.
3. If the data either in statement I alone or in statement II alone is sufficient to answer the question.
4. If the data in both statements I and II together is necessary.

Answer: If the data either in statement I alone or in statement II alone is sufficient to answer the question.

Each statement independently provides sufficient information to determine who sits at the extreme end of the row. Either statement alone is enough.

Q27. 7 friends in a row, all facing north. Who sits in the middle? I. Three friends between O and N. None at extreme ends. II. N sits second left of S. Q sits third right of S.

1. Data in statement I alone sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.
2. Data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.
3. Data in both the statements I and II together are necessary to answer the question.
4. Data in both the statements I and II together are not sufficient to answer the question.

Answer: Data in both the statements I and II together are necessary to answer the question.

Statement I: 3 between O and N (not at extremes) gives a relative arrangement but multiple absolute positions possible. Statement II: N,S,Q fixed but O,M,R,P unplaced. Both together pin all 7 positions, revealing the middle seat.

Q28. In which direction is U from R? I. Q is 25m north-west of R. U is directly north of Q and directly west of R. II. [Additional constraints about positions]

1. Only I is sufficient.
2. Only II is sufficient.
3. Both I and II together are sufficient.
4. Neither I nor II is sufficient.

Answer: Only I is sufficient.

Statement I: Q is NW of R. U is directly north of Q AND directly west of R. If U is west of R and north of Q (which is already NW of R), then U is north or northwest of R. Statement I alone sufficiently determines U's direction from R.